I just found out about the Desmos online graphing calculator, and it is really a very nice tool. Just while playing with it, I had the idea of creating simulations. I decided to make a simulation of the ray daigrams of the convex mirrors. I tried twice and I failed twice. But I cannot find the cause. I have checked every calculation about 3 times and still I cannot make it.

But let me tell the main problem. In my fist simulation, I found out that when I used the basic laws of reflection (i=r), The ray parellel to the principal axis does not meet the axis at the focus. Example:


In this image, we can see that when the ray is at height of 0.5 (units), the ray passes the principal axis just before the focus.

In the second simulation, I used the laws of drawing the ray diagrams as given in my book.

  1. A ray that is parallel to the principle axis, on reflection will pass through the focus.
  2. A ray through the center retraces its path in the opposite direction after reflection.

In this one, the problem comes when the object is placed at the Center of curvature. According to my physics book, the image should be formed at C and it should be of the same size as the object. Here the image is formed at C but the image is larger than the object.


In this image we can see that the object is 0.6 units high but the image is 1 unit.

Here are the links to the simulations:

  1. https://www.desmos.com/calculator/xjyhunca0o
  2. https://www.desmos.com/calculator/xrvkqxkvbz

I'm sorry, I did not show my calculation of the equations in the simulations but they can be derived very easily.

So then where did I go wrong? Why am I not getting the correct answer??


1 Answer 1


The rays will only come exactly to the focus if you're using a parabolic mirror. A spherical mirror is considered a good compromise for limited fields of view (plus it's got the advantage of behaving the same off-axis as on-axis).

Your second setup is invalid, I believe. You need to differentiate between the object's position (or height) and the height of both rays as they reach the mirror. I may have misunderstood your diagram, in which case I apologize.

  • $\begingroup$ So then Is my book wrong that any ray parellel to the axis will converge at the focus? I have read this in many books, why do they write it? $\endgroup$
    – Kartik
    Sep 19, 2014 at 14:50
  • 2
    $\begingroup$ @Kartik That is true for a parabolic mirror. In practice, a sphere is approximately a parabola if you are close to the optical axis, and your textbooks don't distinguish between the two. If you want to fix your simulation you can either 1) use a significantly larger circle or 2) trade out the circle for a parabola. $\endgroup$ Sep 19, 2014 at 15:25

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